Related papers: Dynamics of Gravity-Capillary Solitary Waves in De…
We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general…
We consider the gravity-capillary water waves problem in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features. Namely, we consider a variable bottom, smooth obstacles in the flow and a constant…
We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the…
A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is considered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then…
We consider the two-dimensional capillary water waves with nonzero constant vorticity in infinite depth. We first derive the Babenko equation that describes the profile of the solitary wave. When the velocity $c$ is close to a critical…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
We report experimental results on nonlinear wave coupling in surface wave turbulence on water at scales close to the crossover between surface gravity waves and capillary waves. We study 3-wave correlations either in the frequency domain or…
We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…
We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve 3-wave…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
While several articles have been written on water waves on flows with constant vorticity, little is known about the extent to which a nonconstant vorticity affects the flow structure, such as the appearance of stagnation points. In order to…
We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this…
We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves…
We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green-Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duch{\^e}ne, Israwi…
We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it…
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless…